Highly divisible triangular number

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28

We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

---

Idea

A problem of 'factor decomposition'

Brute force.

---

def decompose(number):
    factors = [1, number]
    d = 2
    while pow(d, 2) < number:
        if number % d == 0:
            factors.extend([d, number // d])
        d += 1
    return factors

decompose(28)

[1, 28, 2, 14, 4, 7]

def generate_triangle_number():
    i = 1
    while True:
        yield i * (i + 1) // 2
        i += 1

def solve(divisor_number):
    for triangle_number in generate_triangle_number():
        # result triangle number must greater than pow(divisor_number, 2)
        if triangle_number < pow(divisor_number, 2):
            continue
        if len(decompose(triangle_number)) > divisor_number:
            return triangle_number

solve(5)

28

solve(500)

76576500